"completed his time":
No, it doesn't mean that he died. Looking at the original, this whole sentence is very convoluted and seems to almost be a literal translation of the Portuguese. It means that he "served his time", meaning that he had served enough in the past to be given some position of responsibility.
"Hollanders went hauling on warps":
"Warps" are ropes which are attached to stationary objects. Here, the Dutch are pulling on the warps, or ropes, with grappling hooks on the end, which they have thrown or fired onto the enemy ship, which they then use to pull their ship alongside the other.
"driving in the teeth of":
This phrase seems to be a literal translation again. I've never heard of the idiom "the teeth of the ship" in English. You do get a sense of meaning though, in that the pressure of the ice floes are in danger of crushing the ship.
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